The partial matrix elements (REF ) and (REF ) have a simple pole
located at \(p_{\text{pol}} = i r_{0}^{-1}\exp \left(-\pi A/\Gamma \right) = i p_{\max }\) . According to the theory of scattering [1]}, [2]}, a pole of an
elastic partial element of the \(S\) -matrix located at a positive imaginary
momentum corresponds to a bound state.
In our case, however, the presence of the pole is only an artifact of the
used approach.
Indeed, this pole exists for arbitrary small values of \(h\)  and \(r_{0}\) , which
is impossible for bound states.
We also failed to find fermion bound states in the partial channels with \(m= \pm 1\)  using numerical methods.
